A process for manufacturing a single crystal ingot (a single crystal) of a specified substance, such as a semiconductor material, by the Czochralski method (the “pulling method”) will be taken as a typical example of a controlled object in a time variant system with a dead time, and will be explained in the following.
It goes without saying that, in manufacture of a single crystal ingot by the Czochralski method or by another method, it is extremely important to reduce the crystal defects in the single crystal ingot. Furthermore, it is also extremely important to control the diameter of the straight body portion of the single crystal ingot fixedly to the desired value. In order better to satisfy these demands, for example, control methods such as the following have been proposed.
In Patent Document #1 a method is disclosed for, in the Czochralski method, keeping the diameter of the straight body portion of the single crystal ingot constant, and for suppressing the occurrence of polycrystals. According to this method, while pulling up the single crystal ingot and forming the straight body portion, the weight of the single crystal ingot is measured, and the current external diameter value of the single crystal ingot is calculated from this measured weight. Based upon this calculated current external diameter value, and upon the response function of a prediction model (for example, a step response model) which is set up in advance, an external diameter predicted value for the single crystal ingot after the lapse of a predetermined time period is calculated. This calculated external diameter predicted value and the specified external diameter target value are compared together and the deviation between them is calculated, and the output of the heater is controlled according to this deviation.
Moreover, a control method in which the control method disclosed in Patent Document #1 is improved is disclosed in, for example, Patent Document #2. According to this method, the time constant or gain of the response function of the prediction model described above is adjusted, so as to decrease monotonically along with the passage of time.
And, in Patent Document #3, there is disclosed a method of, in the Czochralski method, growing the increased diameter portion (the cone portion or shoulder portion) of the single crystal ingot, in order to ensure that the crystallinity of the straight body portion of the single crystal ingot is not disturbed. According to this method, while the cone portion is being grown, the rate of change of the diameter of the cone portion and the temperature of the melt are measured. The measured rate of change of the diameter of the cone portion and a target value which is set in advance are compared together, and a temperature target value is adjusted according to the difference between them. This adjusted temperature target value and the measured melt temperature are compared together, and the electrical power supplied to the heater is PID controlled according to the deviation between them.    Patent Document #1: Japanese Patent No. 2,813,439    Patent Document #2: Japanese Laid-Open Patent Publication Heisei 9-165293    Patent Document #3: Patent Publication 7-77996